
Using the properties of the stochastic integrals ([1]}, pp.132-133), we have the following estimate:
\(J_1 \le \sum _{k=1}^{\infty } \gamma _k^2 \lambda _k^2 \int _{0}^{t_1} \left(e^{-\lambda _k(t-s)} - e^{-\lambda _k(t_1-s)}\right)^2 ds = \sum _{k=1}^{\infty } \gamma _k^2 \lambda _k^2 \int _{0}^{t_1} \left(\int _{t_1-s}^{t-s} - \lambda _k e^{-\lambda _k \tau } d\tau \right)^2\) 
\(= \sum _{k=1}^{\infty } \gamma _k^2 \lambda _k^2 \int _{0}^{t_1} \left(\int _{t_1-s}^{t-s} - \lambda _k \tau e^{-\lambda _k \tau } \frac{1}{\tau } d\tau \right)^2 ds \le C_0 \sum _{k=1}^{\infty } \gamma _k^2 \lambda _k^2 \int _{0}^{t_1} \left(\int _{t_1-s}^{t-s} \frac{d\tau }{\tau } \right)^2 ds.\) 
